*DECK ELMBAK SUBROUTINE ELMBAK (NM, LOW, IGH, A, INT, M, Z) C***BEGIN PROLOGUE ELMBAK C***PURPOSE Form the eigenvectors of a real general matrix from the C eigenvectors of the upper Hessenberg matrix output from C ELMHES. C***LIBRARY SLATEC (EISPACK) C***CATEGORY D4C4 C***TYPE SINGLE PRECISION (ELMBAK-S, COMBAK-C) C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK C***AUTHOR Smith, B. T., et al. C***DESCRIPTION C C This subroutine is a translation of the ALGOL procedure ELMBAK, C NUM. MATH. 12, 349-368(1968) by Martin and Wilkinson. C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 339-358(1971). C C This subroutine forms the eigenvectors of a REAL GENERAL C matrix by back transforming those of the corresponding C upper Hessenberg matrix determined by ELMHES. C C On INPUT C C NM must be set to the row dimension of the two-dimensional C array parameters, A and Z, as declared in the calling C program dimension statement. NM is an INTEGER variable. C C LOW and IGH are two INTEGER variables determined by the C balancing subroutine BALANC. If BALANC has not been C used, set LOW=1 and IGH equal to the order of the matrix. C C A contains the multipliers which were used in the reduction C by ELMHES in its lower triangle below the subdiagonal. C A is a two-dimensional REAL array, dimensioned A(NM,IGH). C C INT contains information on the rows and columns interchanged C in the reduction by ELMHES. Only elements LOW through IGH C are used. INT is a one-dimensional INTEGER array, C dimensioned INT(IGH). C C M is the number of columns of Z to be back transformed. C M is an INTEGER variable. C C Z contains the real and imaginary parts of the eigenvectors C to be back transformed in its first M columns. Z is a C two-dimensional REAL array, dimensioned Z(NM,M). C C On OUTPUT C C Z contains the real and imaginary parts of the transformed C eigenvectors in its first M columns. C C Questions and comments should be directed to B. S. Garbow, C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY C ------------------------------------------------------------------ C C***REFERENCES B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, C Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen- C system Routines - EISPACK Guide, Springer-Verlag, C 1976. C***ROUTINES CALLED (NONE) C***REVISION HISTORY (YYMMDD) C 760101 DATE WRITTEN C 890831 Modified array declarations. (WRB) C 890831 REVISION DATE from Version 3.2 C 891214 Prologue converted to Version 4.0 format. (BAB) C 920501 Reformatted the REFERENCES section. (WRB) C***END PROLOGUE ELMBAK C INTEGER I,J,M,LA,MM,MP,NM,IGH,KP1,LOW,MP1 REAL A(NM,*),Z(NM,*) REAL X INTEGER INT(*) C C***FIRST EXECUTABLE STATEMENT ELMBAK IF (M .EQ. 0) GO TO 200 LA = IGH - 1 KP1 = LOW + 1 IF (LA .LT. KP1) GO TO 200 C .......... FOR MP=IGH-1 STEP -1 UNTIL LOW+1 DO -- .......... DO 140 MM = KP1, LA MP = LOW + IGH - MM MP1 = MP + 1 C DO 110 I = MP1, IGH X = A(I,MP-1) IF (X .EQ. 0.0E0) GO TO 110 C DO 100 J = 1, M 100 Z(I,J) = Z(I,J) + X * Z(MP,J) C 110 CONTINUE C I = INT(MP) IF (I .EQ. MP) GO TO 140 C DO 130 J = 1, M X = Z(I,J) Z(I,J) = Z(MP,J) Z(MP,J) = X 130 CONTINUE C 140 CONTINUE C 200 RETURN END